Algebra

Matrices & Determinants

Medium

core

Match List-I with List-II

List-I List-II
(A) The number of possible matrices of order 3x3 with each entry 1 or 0 (I) $2^4$
(B) The number of possible matrices of order 2x3 with each entry 1 or 0 (II) $2^9$
(C) The number of possible matrices of order 2x3 with each entry 0,1,2 (III) $2^6$
(D) The number of possible matrices of order 2x2 with each entry 1 or 0 (IV) $3^6$

Choose the correct answer from the options given below:

List-I	List-II
(A) The number of possible matrices of order 3x3 with each entry 1 or 0	(I) $2^4$
(B) The number of possible matrices of order 2x3 with each entry 1 or 0	(II) $2^9$
(C) The number of possible matrices of order 2x3 with each entry 0,1,2	(III) $2^6$
(D) The number of possible matrices of order 2x2 with each entry 1 or 0	(IV) $3^6$

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (III), (B) - (I), (C) - (IV), (D) - (II)

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

✅ Correct Option: 1

The number of possible matrices with given constraints can be found using:

Number of possible matrices = (choices per entry) $^{\text{(total entries)}}$

For a matrix with dimensions rows × columns:

Total entries = rows × columns

Each entry can be filled independently with the given choices.

(A) 3×3 matrix with entries 0 or 1

Total entries = 3 × 3 = 9

Choices per entry = 2

Number of possible matrices = $2^9$

Therefore, (A) matches with (II)

(B) 2×3 matrix with entries 0 or 1

Total entries = 2 × 3 = 6

Choices per entry = 2

Number of possible matrices = $2^6$

Therefore, (B) matches with (III)

Total entries = 2 × 3 = 6

Choices per entry = 3

Number of possible matrices = $3^6$

Therefore, (C) matches with (IV)

(D) 2×2 matrix with entries 0 or 1

Total entries = 2 × 2 = 4

Choices per entry = 2

Number of possible matrices = $2^4$

Therefore, (D) matches with (I)

Final matching:

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

2025: 22 May Shift 2

Let A and B be 3×3 matrices such that $A \neq B$ . If $A^3 = B^3$ and $A^2B = B^2A$ , then the determinant of $A^2 + B^2$ is:

2025: 15 May Shift 2

If $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = k \cdot a^l b^m c^n$ , then

Match List-I with List-II

List-I	List-II
(A) $l = m = n =$	(I) 10
(B) $k + l + m + n =$	(II) 6
(C) $k^2 + l^2 + (m - n)^2 =$	(III) 2
(D) $l^2 + m^2 + (n - k) =$	(IV) 20

Choose the correct answer from the options given below:

2022: 6 Aug Shift 2

If A is a square matrix of order 3 and $|adj A| = 49$ , then $|7A^{-1}|^2$

2025: 2 June Shift 1

If $a_{ij}=i+3j$ , then the matrix of order 2 with elements as $a_{ij}$ is

2026: 31 May Shift 2

If $\begin{bmatrix} 0 & x \\ 2 & 1 \end{bmatrix} + 2\begin{bmatrix} 3 & 1 \\ y & 0 \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 8 & 1 \end{bmatrix}$ , then the value of $2x+3y$ is :

2026: 22 May Shift 1

If $A=\begin{bmatrix}1 & 1 & 1\\1 & 0 & 3\\1 & -2 & 1\end{bmatrix}$ , then

Match List-I with List-II

List-I	List-II
(A) $\lvert A\rvert$	(I) 48
(B) $\lvert 2A\rvert$	(II) 36
(C) $\left\lvert\operatorname{adj}(A)\right\rvert$	(III) 12
(D) $2\lvert A\rvert$	(IV) 6

Choose the correct answer from the options given below:

Solution

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